Thousands of South Koreans took to the streets of the capital on Saturday calling for increasingly unpopular president Park Geun-hye to step down over allegations that she let an old friend, the daughter of a religious cult leader, interfere in important state affairs. The evening protest came after Park ordered 10 of her senior secretaries to resign over a scandal that is likely to deepen the president’s lame duck status ahead of next year’s election.

Holding candles and signs reading “Who’s the real president?” and “Park Geun-hye, step down”, the protesters marched through downtown Seoul after holding a candlelight vigil near City Hall. Police estimated that about 12,000 people turned out for the biggest anti-government demonstration in Seoul in months.

Park ordered 10 of her senior secretaries to resign after she admitted letting an old friend and the daughter of a religious cult leader to interfere in important state affairs.

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Park has been facing calls to reshuffle her office after she admitted on Tuesday that she had provided longtime friend Choi Soon-sil drafts of her speeches for editing. Her televised apology sparked huge criticism about her mismanagement of national information. She had already become unpopular for what some saw as a heavy-handed leadership style and lack of transparency.

There has also been media speculation that Choi, who holds no government job, meddled in government decisions on personnel and policy, and exploited her ties with the president to misappropriate funds from nonprofit organisations.

The saga, triggered by weeks of media reports, has sent Park’s approval ratings to record lows and the minority opposition Justice party has called for her to resign.

South Korean President Park Geun-hye has offered a public apology after a South Korean TV network reported reported that Choi Soon-sil, who has no official governmental position, was informally involved in editing some of Park’s key speeches. Photograph: Handout/Getty Images

“Park has lost her authority as president and showed she doesn’t have the basic qualities to govern a country,” Jae-myung Lee, from the opposition Minjoo party and the mayor of the city of Seongnam, told the protesters from a stage on Saturday.

Prosecutors on Saturday widened their investigation by searching the homes of presidential officials suspected of interacting with Choi and receiving their office files from the Blue House the presidential office and residence. Prosecutors had previously summoned some of Choi’s key associates and raided their homes and workplaces, as well as the offices of two nonprofit foundations Choi supposedly controlled.

Among the aides to have been expelled are Woo Byung-woo, senior presidential secretary for civil affairs, and Ahn Jong-beom, senior secretary for policy coordination. Lee Won-jong, Park’s chief of staff, tendered his resignation on Wednesday. Park’s office said she plans to announce a new lineup of senior secretaries soon.

Choi’s lawyer, Lee Gyeong-jae, told reporters on Friday that she is currently in Germany and is willing to return to South Korea if prosecutors summon her. In an interview with a South Korean newspaper earlier this week, Choi admitted receiving presidential documents in advance, but denied intervening in state affairs or pressuring companies into donating to the foundations.